There is not really a justifiable reason for Myles Straw to continue to see regular playing time. Straw is not anything resembling a force at the plate and there are other options that the Guardians should be giving playing time to over him. Much like the recent trade of Amed Rosario, Straw should be moved in order to make Terry Francona go to someone else as the option to man center field on a daily basis.
When it comes to Straw it would be one thing if he was being used as a fourth outfielder, defensive replacement, pinch runner type. Unfortunately, this has not been his role in Cleveland. Being unable to find a consistent option in the outfield has led to increased playing time that he otherwise should not be afforded.
As far as interest from other teams, selling them on Straw being what he should be as an option off the bench could be enticing. There is no future in Cleveland and they need to find a way to part ways before they are forced into having to release him. Getting something, even if it is just cash considerations, is better than getting nothing at all.